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To determine the equation of the line in slope-intercept form \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept, you can use the given information:

- **Slope \(m = -\frac{1}{3}\)**
- **Y-intercept \(b = 1\)** (because the y-intercept is at \((0, 1)\))

Now, substitute these values into the slope-intercept form equation:

\[
y = -\frac{1}{3}x + 1
\]

So, the equation of the line is:

\[
y = -\frac{1}{3}x + 1
\]

Would you like further details or have any questions about this solution?

Here are 5 related questions to expand your understanding:
1. What does the slope of a line tell us about its direction?
2. How do you convert the equation of a line from slope-intercept form to standard form?
3. What would the graph of this line look like?
4. How do you find the x-intercept of this line?
5. What happens to the equation if the slope changes to a positive value?

**Tip:** The slope \(m\) determines how steep the line is and whether it rises or falls. A negative slope means the line goes downwards as you move from left to right.

Determine the equation of the line in slope-intercept form with the slope of -1/3 and y-intercept at (0, 1).

Learn how to determine the equation of a line with a slope of -1/3 and a y-intercept at (0, 1) in slope-intercept form. This problem uses the equation y = mx + b, where m is the slope and b is the y-intercept. Suitable for students in Grades 8-10.

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